Example 5: Functions Within a Closed Interval

Let g be the function whose domain is the closed interval [1, 2] with the rule

g(x) = x².

The domain and rule can be written in concise form with an equation and extra inequalities,

g(x) = x²,     1 ≤ x ≤ 2.

Note that

g(0) is undefined,     g(1) = 1,

g(2) = 4,     g(3) is undefined.

The graph is described by the formulas

y = x², 1 ≤ x ≤ 2

and is drawn in Figure 1.2.7.